连续时间金融市场模型的解析解
Analytic solutions in a continuous-time financial market model
摘要：
提出了一个连续时间下的异质代理市场模型。市场上充斥着基本面交易者和图表分析师，他们都使用简单的线性交易规则。大多数相关文献探讨了稳定性，价格动态和盈利能力，无论是在确定性模型或模拟。我们的新配方本身的分析治疗，即使在随机的情况下。我们证明的条件（随机）稳定的价格过程，也为价格均值恢复到基本价值。假设稳定性，我们推导出分析公式的人口比例如何影响价格动态和盈利能力的战略。我们的研究结果表明，无论哪种交易者类型在市场上出现的更多，都会获得更高的回报。
英文摘要：
We propose a heterogeneous agent market model (HAM) in continuous time. The market is populated by fundamental traders and chartists, who both use simple linear trading rules. Most of the related literature explores stability, price dynamics and profitability either within deterministic models or by simulation. Our novel formulation lends itself to analytic treatment even in the stochastic case. We prove conditions for the (stochastic) stability of the price process, and also for the price to mean-revert to the fundamental value. Assuming stability, we derive analytic formulae on how the population ratios influence price dynamics and the profitability of the strategies. Our results suggest that whichever trader type is more present in the market will achieve higher returns.
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